Problem: In triangle $ABC$, $AB = 16$, $AC = 24$, $BC = 19$, and $AD$ is an angle bisector.  Find the ratio of the area of triangle $ABD$ to the area of triangle $ACD$.  (Express your answer as a fraction in lowest terms.)
Solution: The ratio of the area of triangle $ABD$ to the area of triangle $ACD$ is $BD/CD$.  By the angle bisector theorem, $BD/CD = AB/AC = 16/24 = \boxed{\frac{2}{3}}$.